Download Novel approaches of data-mining in experimental physics

XXIV International Symposium on
Nuclear Electronics & Computing
Varna, 09-16 September, 2013.
Novel approaches of
data-mining in
experimental
physics
G.A.Ososkov,
Laboratory of Information Technologies
Joint Intstitute for Nuclear Research,
141980 Dubna, Russia
email: [email protected]
http://www.jinr.ru/~ososkov
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Data mining concept
Classical approaches for processing experimental data supposed to
have a model describing a physical system and based on the advanced
physical theory. Then observed data are used to verify the underlying
models and to estimate its direct or indirect parameters.
 Now, when the experimental data stream is terabytes/sec, we come
to the BIG DATA era, having often a lack of the corresponding
theory, our data handling paradigm shifts from classical modeling and
data analyses to developing models and the corresponding analyses
directly from data. (Data-driven detector alignment as an example)
 The entire process of applying a computer-based methodology,
including new techniques, for discovering knowledge from data is
called data mining.

Wikipedia: “-it is the analysis of large amounts of data about
experimental results held on a computer in order to get information
about them that is not immediately available or obvious.”
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Data mining methods
It is the process of extracting patterns from large data sets by combining methods
from statistics and artificial intelligence with database management.
Data mining commonly involves four classes of tasks:
 Association rule learning – searches for relationships between variables.
 Clustering – is the task of discovering groups and structures in the data that are in
some way or another "similar", without using known structures in the data.
 Classification – is the task of generalizing known structure to apply to new data.
 Regression – attempts to find a function which models the data with the least error
Although Data Mining Methods (DMM) are oriented mostly on mining business and
social science data, in recent years, data mining has been used widely in the areas of
science and engineering, such as bioinformatics, genetics, medicine, education and
electrical power engineering. So a great volume of DMM software is now exists as
open-source and commercial. However one would not find experimental physics in
DMM application domains.
Therefore we are going to understand how DMM would look
like, if data will be taken from high energy physics?
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Data mining peculiarities
for experimental high energy physics (HEP)
Let us consider some examples
Condensed
Barion
Matter
1. СВМ experiment
TRD
RICH
(Germany, GSI, to be
running in 2018)
107 events per sec,
~1000 tracks per event
~100 numbers per track
Total: terabytes/sec !
RICH - Cherenkov
radiation
detector
simulated event of the central Au+Au
collision in the vertex detector
schematic view of the СВМ setup
Our problem is to recognize all of these rings
and evaluate their parameters despite of their
overlapping, noise and optical shape distortions
view of Cherenkov radiation rings
registered by the CBM RICH detector
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2. Transition radiation detector (TRD)
TR Production
TRD measurements allow for each particle to
reconstruct its 3D track and calculate its
energy loss (EL) during its passage through
all 12 TRD stations in order to distinguish
electrons e- from pions π± .
Unlike π±, electrons generate additionally the
transition radiation (TR) in TRD.
Our problem is to use the distributions of EL+TR for e- and
π± in order to test hypothesis about a particle attributing
to one of these alternatives keeping the probability α of the
1st kind of error on the fixed level α =0.1 and the probability
β of the 2nd kind of error on the level less than β< 0.004.
Both distributions were simulated by special program GEANT-4 taking into account all
details of the experimental setup and corresponding physical assumptions related to
heavy ion collisions. However the test based on direct cut on the sum of energy losses
could not satisfy these requirements because both EL and TR have long-tailed
Landau distributions.
The main lesson: a transformation needed to reduce Landau tails of EL
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Example 3: the OPERA experiment
CERN
LNGS: the world largest underground physics laboratory
Neutrino beam
Search for neutrino
oscillations
LNGS
1600 m in depth
~100’000 m3 caverns’ volume
OPERA
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A. Ereditato - LNGS - 31 May 2010
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the OPERA experiment:
Search for neutrino
oscillations (OPERA is running)
Hadron shower axix
Each wall is accompanied by two planes of
electronic trackers made of scintillator strips
The crucial issue in OPERA is finding of that
particular brick where the neutrino
interaction takes place. Tracks formed by
scintillator hits should originate from a single
point - vertex.
However the main obstacle is back-scattered
particles (BSP) occuring in 50% of events,
which do not contain useful information.
Emulsion scanning to determine neutrino
oscillation – is the separate task out of this talk
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BSP
Real vertex
Two types of OPERA events with BSP
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The particular features of the data
from these detectors are as follows:





data arrive with extremely high rate;
recognized patterns are discrete and have complex texture;
very high multiplicity of objects (tracks, Cherenkov radiation rings,
showers) to be recognized in each event;
the number of background events, which are similar to “good”
events, is larger than the number of the latter events by several
orders of magnitude;
noise counts are numerous and correlated.
——————————————————————————————--—————-
The basic requirements to data processing in current experiments are:
maximum speed of computing in combination with the highest
attainable accuracy and high efficiency of methods of estimating
physical parameters interesting for experimentalists.
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Data mining in experimental HEP 1.
To understand the need for analyses of large, complex,
information-rich data sets in HEP let us start from
considering stages of HEP data processing
1. Pre-processing is very important stage. It includes:
Data acquisition: before data mining algorithms can be used, a
target data set must be assembled and converted from the rough
format of detector counters into natural unit format.
 Data Transformation: to transform data into forms appropriate for
mining, they must be corrected from detector distortions and
misalignment by special calibration and alignment transformation
procedures.
 Data selection: then data must be cleaned to remove noisy,
inconsistent and other observations, which do not satisfy acceptance
conditions. It can be accomplished in a special often quite sophisticate
triggering procedure that usually causes a significant reduction of
target data (several orders of magnitude).

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Data mining in experimental HEP 2.
2. HEP data processing involves following stages and
methods:
Pattern recognition: hit detection, tracking, vertex finding, revealing
Cherenkov rings , fake objects removing etc employing the following
methods:
 Cluster analysis
 Hough transform
 Kalman filter
 Neural networks
 Cellular automata
 Wavelet analysis
The next expounding will be
 Physical parameters estimation
some retrospections of the
- robust M-estimations
JINR experience to illustrate
 Hypothesis testing
HEP data processing steps
- Likelihood ratio test
- Neural network approach
- Boosted decision trees

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Data mining in experimental HEP 3.

Monte-Carlo simulations are used on all stages and
allow to
- accomplish in advance the experimental design of a hardware setup and data
mining algorithms and optimize them from money, materials and time point of view;
- develop needed software framework and test it;
- optimize structure and needed equipment of planned detectors minimizing
costs, timing with a proposed efficiency and accuracy;
- calculate in advance all needed distributions or thresholds for goodness-of-fit
tests;
Parallel programming of optimized algorithms is inevitable
 Software quality assurance (SQA) is the very important issue
of any great programming system development
 GRID technologies changed considerably HEP data
processing stages, which now more and more correspond to
the GRID Tier hierarchy.
Since each of theses items needs a long separate
expounding, they will be only briefly noted below

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Some retrospections
Artificial Neural Networks
Why ANN for a contemporary HEP experiment?
1.



historically namely physicists wrote in 80-ties one of the first NN
programing packages – Jetnet. They were also among the first neurochip users
after being trained ANN is one of the most appropriate tools for
implementing many of data handling tasks, while on the basis of
some new physical model physicists have possibility to generate
training samples of any arbitrary needed length by Monte Carlo
appearance of TMVA - Toolkit for Multivariate Data Analysis with
ROOT
Thus, there are many real problems solved on the basis of ANN in
experimental physics as
- Object recognizing and classifying
- Statistical hypothesis testing
- Expert system implementing
- Approximation of many-dimensional functions
- Solution of non-linear differential equations
- etc
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NN application examples: 1. RICH detector
A fragment of photodetector plane. In average there
are 1200 points per event forming 75 rings.
A sketch of the RICH detector
Data processing stages:
 Ring recognition and their parameters evaluation;
 Compensating the optical distortions lead to
elliptic shapes of rings;
 Matching found rings with tracks of particles
which are interesting to physicists
 Eliminating fake rings which could lead to wrong
physical conclusions
 Accomplishing the particle identification with the
fixed level of the ring recognition efficiency
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Electrons
Pions
Radius versus momentum for
reconstructed rings.
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NN for the RICH detector
The study has been made to select the most informative ring features needed to
distinguish between good and fake rings and to identify electrons.
Ten of them have been chosen to be input to ANNs, they are:
1.Number of points in the found ring
2.Its distance to the nearest track
3.The biggest angle between two neighbouring points
4.Number of points in the narrow corridor surrounding ring
5.Radial ring position on the photodetector plane
6.χ2 of ellipse fitting
electrons
7.Both ellipse half-axes (A and B)
8.angle φ of the ellipse inclination to abscissa
9.track azimuth
10. track momentum
40000 e and π rings to train
π-mesons
Two samples with 3000 e (+1)and 3000 π (-1)
have been simulated to train NN. Electron
recognition efficiency was fixed on 90%
Probabilities of the 1-st kind error 0.018
and the 2-d kind errors 0.0004
correspondingly were obtained
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NN application examples:
2. e- / π± separation by transition radiation
Two ideas to avoid obstacles with the easy cut test and long tails of energy
loss (ΔE) distributions:
1. Apply artificial neural network for testing
2. Calculate likelihood ratio for ΔE of each TRD station as input to ANN
We use Monte-Carlo calculations to simulate a representative sample of TRD signals for
given experimental conditions and then obtain energy losses from all n TRD stations for both eand π± , sort them and calculate probability density functions (PDF) for ordered ΔEs. Then we
repeat simulation in order to train neural network with n inputs and one output neuron,
which should be equal +1 in case of electron and and -1 in case of pion. As inputs, the
likelihood ratios for each ΔE were calculated
L
PDF (E )
PDF (E )  PDFe (E )
The result of testing the trained neural network gave
the probability of the 2nd kind of error β= 0.002
It satisfied the required experimental demands.
It is interesting to note: Applying Busted decision
Trees algorithm from TMVA allows to improve pion
suppression result up to 15-20% comparing to NN
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ANN output distribution
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NN application examples: 3. OPERA experiment
To facilitate the vertex location a considerable data preprocessing
has been fulfilled in order to

eliminate or, at least, reduce electronic noise. The method was based on cellular
automaton that rejects points having no nearest neighbours;
 Reconstruct muon tracks (Hough transform, Kalman filter)
 M-estimate hadron shower axis with 2D robust weights taking into account not only
distance of a point to the shower axis, but also amplitudes of scintillator signals
 make a study to determine
15 parameters to
input them to ANN
.
According to 3 classes of events 3 neural networks of MLP type were then trained for
each class on 20000 simulated events to make a decision about the wall with the event
vertex. The wall finding efficiency on the level of 80 – 90% was then calculated by testing
10000 events.
NN results were then used in the brick finding procedure.
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Recurrent ANNs and applications
Hopfield’s theorem: the energy function
E(s) = - ½ Σij si wij sj
of a recurrent NN with the symmetrical weight matrix wij = wji , wii = 0
has local minima corresponding to NN stability points
Applications in JINR
1. Track recognition by Denby- Peterson (1988) segment model with
modifications was successfully used for tracking in the EXCHARM
experiment
2. More rare: track recognition by rotor models of Hopfield networks
E
1
2
ij
1
rij
v v  
m i j
1
2
ij
1
rij
2
(
v
r
)
i ij
m
The energy function: the first term
forces neighbouring rotors to be close to
each other. The second term is in
charge of the same between rotors and
track-segments.
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Our innovations (I.Kisel, 1992)
 cos 2 ij sin 2 ij 
v j  
 v j  W ij v j
 sin 2  ij  cos 2  ij
Therefore we obtain a simple energy function
without any constrains
1
v i  v j
E 
2 ij
This approach has been applied in the ARES experiment with some extra
efforts:
- prefiltering by cellular automaton;
- local Hough algorithm for initial rotor set up;
- special robust multipliers for synaptic weights.
Results: recognition efficiency - 98%
Analysis of ionograms.
Data from the vertical sounding
of the ionosphere
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Up to now the corresponding program is
in use in the Irkutsk Institute of the
terrestrial magnetism, Russia and in the
Lowell University, MA, USA
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Elastic neural networks
ANN drawbacks revealed by physicists in many HEP applications:
▪ too slow convergence of the ANN evolution due to too high degrees of freedom;
▪ only recognition is fulfilled without taking into account the known track model;
▪ over-sensitivity of ANNs to noise is indicated.
Therefore it was suggested to combine both stages: recognition and fitting of a track in
one procedure when deformable templates (elastic arm) formed by equations of particle
motion are all bended in order to overlaid the data from the detector. A routine then has
to evaluate whether or not the template matched a track.
Ohlsson and Peterson (O&P, 1992 ) from the Lund University realized this idea as a
special Hopfield net with the energy function depending from helix parameters
describing a track and binary neurons Sia, each of them is equal to 1 or 0 when i-th point
belongs or not to the a-th track, respectively.
Gyulassy and Harlander (G & H, 1991) proposed their elastic tracking that can
physically be described as interaction between the positively charged template and
negatively charged spatial points measured in the track. The better the elastic template
fits points, the lower the energy of their interaction.
Using Lorenz potential with the time-dependent width
where a is the
maximal distance, at which points are still accredited to this template, b<< a is spatial resolution of
a detector, G & H obtained the energy to be
minimized by helix parameters π
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Elastic neural networks applications
To avoid E(π,t) getting caught in local spurious minima the simulated
annealing iterative procedure is applied. On the first iteration w(t) is taken
for the highest temperature, when E(π,t) has the only one minimum. Then
w(t) is narrowed gradually allowing more and more accurate search of the
global minimum.
G&H elastic tracking was applied for the STAR TPC simulated data with
remarkably high track-finding efficiency (1998)
O&P elastic NNs after corresponding modifications were succesfully applied
for Cherenkov ring search and track reconstructing (1997). Drift chamber
tracks with their left-right ambiguity in magnetic field demanded to invent 2D
neurons Si=(si+, si —) to determine a point to a track accreditation (1998)
Important to note: a homogeneous magnetic field of NICA-MPD project will
make it possible to apply this elastic arm approach for MPD TPC tracking
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Some retrospections
2. Robust estimates for heavy contaminated samples
Why robust estimates?
In all preceeding experimental examples we must solve typical statistics problems of
parameter estimations by sets of measured data.
However we faced with not usual applied statistics, but with special mass production
statistics
Keywords are:

heavy data contamination due to
 noisy measurements;
 measurements from neighbour objects.
need
in very fast algorithms of
 hypothesis testing and
 parameter estimating
Comparison of LSF and robust fit
in case of one point outlier
How to achieve that?
- Robust approach, based on functional weights of each measuremet, preferably parallel
algorithms
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M-estimate formalizm
Instead of LSF with its crucial assumption of residual normality and quadratic
nature of minimized functional we consider P.Huber’s M-estimate, i.e. replace
quadratic functional S(p) to be minimized by L(p,σ)=Σi ρ(εi ), where
measurement error ε is distributed according to J.Tukey's gross-error model
f(ε) = (1-c) φ(ε) + c h(ε), c is a parameter of contamination, φ(ε) is the Gauss
distribution and h(ε)is some long-tailed noise distribution density.
Likelihood equation for the functional L(p,σ)
by denoting
can be modified to the form
which is similar to the normal LSF equations, but with replacement of the
numerical weight coefficients to weight functions w(ε) to be recalculated on
each step of an iterative procedure.
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How to choose the weight function w(ε) ?
For a particular, but important case of the uniform
contamination h(ε)=h0 we found the optimal weights
w(ε)
which polynomial expansion of up to the fourth order
leads to the approximation
It is the famous Tukey's bi-weights,
which are easier to calculate than
optimal ones.
Simulated annealing procedure is used to avoid sticking functional in local minima.
Recall the energy function of G&H elastic tracking
Lorentz potential in this sum plays a role of the
robust functional weight.
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Application examples: 1. Determination of the interaction
vertex position for only two coordinate planes (NA-45)
The target consists of eight 25-μ gold discs.
One of two silicon disk with 1000 track and noise hits.
So, it is impossible to recognize individual tracks.
Tukey biweight function with cT=3 was used.
Iterational procedure converged in five iterations
with the initial approximation taken as the middle of
Z-axis target region.
The results after processing 4000 Pb+Au events
provide satisfactory accuracy of 300 μ along Z-axis
and good local accuracy of a track.
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Application examples: 2.TDC calibration problem (HERA-B)
It is caused by the fact that real track detectors, as drift chambers, for example, are
measuring the drift time in TDC (Time-Digital Converter) counts. So to perform
data processing, TDC counts are to be transferred, first of all, into drift radii. Such a
transformation named calibration is inevitably data-driven, i.e. is carried out
statistically from real TDC data of some current physical run. Here is an impressive
example of the effectiveness of the robust approach.
The fitting problem in such cases is radically different from any common one, since
for every abscissa we have not one, but many
ordinates with different amplitudes. Therefore every
point to be fitted was provided by 2D weight
depending as of this point distance to the fitted
curve, as of its amplitude.
It is shown how a calibration function r(t) can be
obtained by fitting cubic splines to directly 2D
histogram of drift radii versus TDC counts, which
consists of many thousand bins with various
amplitudes.
The fitted spline only for upper part is shown.
A lot of more applications were reported, in particular, for tracking in presence
of δ-electrons in CMS muon endcup
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Some retrospections
3.Wavelet analysis
What are continuous wavelets?
In contrast to the most known mean of signal analysis as Fourier transform, onedimensional wavelet transform (WT) of the signal f(x) has 2D form ,
where the function  is the wavelet, b is a
displacement (time shift), and a is a scale (or frequency). Condition Cψ < ∞ guarantees
the existence of  and the wavelet inverse transform. Due to the freedom in  choice,
many different wavelets were invented.
The family of continuous wavelets with vanishing momenta is presented here by
Gaussian wavelets, which are generated by derivatives of Gaussian function
Most known wavelet G2
is named “the Mexican hat”
The biparametric nature of wavelets renders it possible to analyze simultaneously
both time and frequency characteristics of signals.
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Wavelets can be applied for extracting very special
features of mixed and contaminated signal
An example of the signal with a
localized high frequency part and
considerable contamination
then wavelet filtering is applied
G2 wavelet spectrum of this signal
Filtering works in the wavelet domain by
thresholding of scales, to be eliminated
or extracted, and then by making
the inverse transform
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Filtering results. Noise is removed and high
frequency part perfectly localized.
NOTE: that is impossible by Fourier transform
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Continuous wavelets: pro and contra
PRO: - Using wavelets we overcome background estimation
- Wavelets are resistant to noise (robust)
CONTRA: - redundancy → slow speed of calculations
- nonorthogonality (signal distotres after inverse transform!)
Besides, real signals to be analysed by computer are discrete, in principle
So orthogonal discrete wavelets should be preferable.
Denoising by DWT shrinking
wavelet shrinkage means, certain wavelet
coefficients are reduced to zero:
Our innovation is the adaptive shrinkage, i.e.
λk= 3σk
where k is decomposition level
(k=scale1,...,scalen), σk is RMS of Wψ for this
level (recall: sample size is 2n)
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Small peak finding with coiflets
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NEW: Back to continuous wavelets
Peak parameter estimating by gaussian wavelets
When a signal is bell-shaped one, it can be approximated by
a gaussian
Then it can be derived analytically that its wavelet
transformation looks as the corresponding wavelet with
.
parameters depending
of the original signal parameters.
Thus, we can calculate them directly in the wavelet domain
instead of time/space domain.
The most remarkable point is, we do not need the inverse
transform!
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Estimating peak parameters in G2 wavelet domain
How it works?
Let us have a noisy invariant mass spectrum
1. transform it by G2 into wavelet domain
2. 2. look for the wavelet surface maximum
bmax ,amax .
3. From the formula for
WG2(a,b;x0,σ)g one can derive analytical
expressions for its maximum x0 and
a. max  5 which should correspond to
the found bmax ,amax . Thus we can use
coordinates of the maximum as
estimations of wanted peak parameters
peak has bell-shape form
xˆ0 , aˆ
4. From them we can directly obtain halfwidth
amplitude
ˆ  max W (aˆ 2  ˆ 2 )
A
5
aˆ 2ˆ
and even the integral
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2
ˆ 
aˆ
5
I  A 2
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Application results to CBM invariant mass spectra
Low-mass dileptons (muon channel)
- ω– wavelet spectrum
ω.
Thanks to Anna Kiseleva
ω. Gauss fit
of reco
signal
M=0.7785
σ =0.0125
A=1.8166
Ig=0.0569
ω. Wavelets
M=0.7700
σ =0.0143
A=1.8430
Iw=0.0598
ω-meson
φ-meson
Even φ- and
mesons have been visible


in the wavelet space, so we could extract
their parameters.
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NEW: Example with set of FOPI data
provided by N.Hermann, GSI, Darmstadt, Germany
Wavelets G4 are used. The formula for σ obtaining is σ = amax/3
1
2
3
noise level σ = 0.009
Despite of the very jagged spectrum wavelets give visible peaks with
σ1 = σ3 = 0.013, σ2 = 0.021
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Clustering in data mining
 Clustering is one of important DM task because it allows to seek groups
and structures in the data that are in some way "similar", without using
known structures in the data.
 Clustering methods are widely used in HEP
data processing to find the point of
particle passage through coordinate
plane of some cell-structure detector
 New application of clustering analysis
allows to develop the URQMD fragmentation model
of nuclear collision at relativistic energies. Clusters or nuclear fragments are
generated via dynamical forces between nucleons during their evolution in
coordinate and momentum space
 New two steps clustering method is proposed for BIG DATA. It
accomplishes the quantization of input data by generating so-called Voronoi
partition. The final clustering is done using any conventional methods of
clustering. A new promising watershed clustering algorithm is proposed.
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Parallel programming


Fortunately the common structure of HEP experimental data naturally
organized as the sequence of events gives the possibility for the natural
multithread parallelism by handling events simultaneously on different
processors.
However the requirements of such experiments as the CBM to handle
terabytes of data per second leads to the necessity of parallelism on the
level of each event by so-called SIMDization of algorithms, that demands
their substantial optimization and vectoring of input data.
For instance, in case of CBM TRD and MuCh tracking algorithms we obtain
Resulting speedup of the track fitter
on the Computer with 2xCPUs Intel Core i7 (8 cores in total) at 2.67 GHz
Time [μs/track]
Speedup
1200
-
Optimization
13
92
SIMDization
4.4
3
Multithreading
0.5
8.8
Final
0.5
2400
Initial
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Throughput: 2*106 tracks/s
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Software quality assurance (SQA)


Since software framework of any contemporary HEP experiment is developed by
efforts of international team from thousand collaborants with various programming
skills, software components, they wrote, can inevitably have bags, interconnection
errors or output result different from specified before.
Therefore automation of experimental framework software testing is needed to
provide the following:
- More reliable software, speedup of its development
- Reduce development cycles
- Continues integration and deployment
- High code coverage to test, ideally, all code in the repository
- Not only unit testing but also system test for simulation and reconstruction
However known SQA systems could not be applied directly for these purposes,since
they are based on the theory of reliability methods and suppose to have a highly
qualified team of programmers and testing with immediate failure repairing, while the
most software in our experimental collaborations are written by physicists who are
not highly qualified in programming and are not able to watch over immediate failure
repairing
 For discussion an automatic test system for HEP experiment should perform:
 Report generation for simulation studies;
 Automatic check of output results based on predefined values;
 Nightly monitoring of the simulation results;
 Designed to be modular in order to easy extend and add new histograms

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Conclusion and outlook remarks







Importance of advanced Monte-Carlo simulations
Robust estimates, neural networks and wavelet applications are
really significant for data-mining in HEP
It looks reasonable to provide wavelet analysis tools in ROOT
The focus of developing data mining algorithms in HEP is shifted to
their optimization and parallelization in order to speed them up
considerably while keeping their efficiency and accuracy
Parallelism is to be introduced inevitably on the basis of new
technologies of computing and software
Software reliability concept is very essential
Distributed or cloud computing are growing. In HEP it is
accomplished by GRID technologies
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Thanks for your attention!
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SQA example for FAIR GSI
SQA general structure
Histogram Creator. It realizes the management of large number of
histograms
2. Drawer. Feature extractor. Report generator. Result checker.
They provide
- Base classes for simulation and study report generation;
- Base functionality for histogram drawing;
- Base functionality for serializing/deserializing images to/from
XML/JSON
- Report in HTML, text, Latex
3. SQA monitoring (SQAM) Its features allow users to easy increase number
of tests for different collision systems, energies, detector geometries etc
SQAM provides:
- Automatic testing of simulation, reconstruction and analysis
- Automatic check of simulation results
QAM current status:
About 30 tests run nightly.
1.
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